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Which of the following expressions is a fourth root of unity? a.) -1 b.) i c.) -i d.) all of the above

Annie Barnes

in Mathematics

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Donald Ward on October 21, 2018

We need to evaluate the fourth roots of unity.For each natural number say, 'n', there are exactly n nth roots of the unity that is expressed in the form as where k=0,1,2,.... n-1Since we have to evaluate the fourth root of the drive.Therefore, we take k=0,1,2 and 3 and n=4So, we obtain Now, For k=0, we get our first root:First root = 1Now, for k=1, we get (Eulers Formula)To, Well, the second root = ow, for k=2, we get (Eulers Formula)Thus, the Third root = -1Now, for k=3, we obtain (Eulers Formula)To, as Well, of the fourth root - = - iHence, all the fourth roots of unity are 1, i, -1 and -iTherefore, the option D is correct, as all the given roots in the option a, B, and C are the fourth roots of unity.


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